Ratio from a Perfect Square's Digit Groups
Number Theory · 25th PMO Qualifying Stage
A five-digit perfect square number $\overline{ABCDE}$, with $A$ and $D$ both nonzero, is such that the two-digit number $\overline{DE}$ divides the three-digit number $\overline{ABC}$. If $\overline{DE}$ is also a perfect square, what is the largest possible value of $\overline{ABC}/\overline{DE}$?
A$23$
B$24$
C$25$
D$26$